Optimal. Leaf size=26 \[ \frac {e^{\frac {1}{5 \left (10+e^{1+e^{e^x}}\right ) x}}}{x^3} \]
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Rubi [F] time = 18.78, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {e^{\frac {2}{100 x+10 e^{1+e^{e^x}} x}} \left (-10-1500 x-15 e^{2+2 e^{e^x}} x+e^{1+e^{e^x}} \left (-1-300 x-e^{e^x+x} x\right )\right )}{500 x^5+100 e^{1+e^{e^x}} x^5+5 e^{2+2 e^{e^x}} x^5} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{\frac {1}{5 \left (10+e^{1+e^{e^x}}\right ) x}} \left (-10-1500 x-15 e^{2+2 e^{e^x}} x+e^{1+e^{e^x}} \left (-1-300 x-e^{e^x+x} x\right )\right )}{5 \left (10+e^{1+e^{e^x}}\right )^2 x^5} \, dx\\ &=\frac {1}{5} \int \frac {e^{\frac {1}{5 \left (10+e^{1+e^{e^x}}\right ) x}} \left (-10-1500 x-15 e^{2+2 e^{e^x}} x+e^{1+e^{e^x}} \left (-1-300 x-e^{e^x+x} x\right )\right )}{\left (10+e^{1+e^{e^x}}\right )^2 x^5} \, dx\\ &=\frac {1}{5} \int \left (-\frac {e^{1+e^{e^x}+\frac {1}{5 \left (10+e^{1+e^{e^x}}\right ) x}}}{\left (10+e^{1+e^{e^x}}\right )^2 x^5}-\frac {10 e^{\frac {1}{5 \left (10+e^{1+e^{e^x}}\right ) x}}}{\left (10+e^{1+e^{e^x}}\right )^2 x^5}-\frac {300 e^{1+e^{e^x}+\frac {1}{5 \left (10+e^{1+e^{e^x}}\right ) x}}}{\left (10+e^{1+e^{e^x}}\right )^2 x^4}-\frac {15 e^{2 \left (1+e^{e^x}\right )+\frac {1}{5 \left (10+e^{1+e^{e^x}}\right ) x}}}{\left (10+e^{1+e^{e^x}}\right )^2 x^4}-\frac {1500 e^{\frac {1}{5 \left (10+e^{1+e^{e^x}}\right ) x}}}{\left (10+e^{1+e^{e^x}}\right )^2 x^4}-\frac {e^{1+e^{e^x}+e^x+\frac {1}{5 \left (10+e^{1+e^{e^x}}\right ) x}+x}}{\left (10+e^{1+e^{e^x}}\right )^2 x^4}\right ) \, dx\\ &=-\left (\frac {1}{5} \int \frac {e^{1+e^{e^x}+\frac {1}{5 \left (10+e^{1+e^{e^x}}\right ) x}}}{\left (10+e^{1+e^{e^x}}\right )^2 x^5} \, dx\right )-\frac {1}{5} \int \frac {e^{1+e^{e^x}+e^x+\frac {1}{5 \left (10+e^{1+e^{e^x}}\right ) x}+x}}{\left (10+e^{1+e^{e^x}}\right )^2 x^4} \, dx-2 \int \frac {e^{\frac {1}{5 \left (10+e^{1+e^{e^x}}\right ) x}}}{\left (10+e^{1+e^{e^x}}\right )^2 x^5} \, dx-3 \int \frac {e^{2 \left (1+e^{e^x}\right )+\frac {1}{5 \left (10+e^{1+e^{e^x}}\right ) x}}}{\left (10+e^{1+e^{e^x}}\right )^2 x^4} \, dx-60 \int \frac {e^{1+e^{e^x}+\frac {1}{5 \left (10+e^{1+e^{e^x}}\right ) x}}}{\left (10+e^{1+e^{e^x}}\right )^2 x^4} \, dx-300 \int \frac {e^{\frac {1}{5 \left (10+e^{1+e^{e^x}}\right ) x}}}{\left (10+e^{1+e^{e^x}}\right )^2 x^4} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.34, size = 26, normalized size = 1.00 \begin {gather*} \frac {e^{\frac {1}{5 \left (10+e^{1+e^{e^x}}\right ) x}}}{x^3} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.77, size = 29, normalized size = 1.12 \begin {gather*} \frac {e^{\left (\frac {1}{5 \, {\left (x e^{\left ({\left (e^{\left (x + e^{x}\right )} + e^{x}\right )} e^{\left (-x\right )}\right )} + 10 \, x\right )}}\right )}}{x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 21, normalized size = 0.81
method | result | size |
risch | \(\frac {{\mathrm e}^{\frac {1}{5 \left ({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}+1}+10\right ) x}}}{x^{3}}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -\frac {1}{5} \, \int \frac {{\left (15 \, x e^{\left (2 \, e^{\left (e^{x}\right )} + 2\right )} + {\left (x e^{\left (x + e^{x}\right )} + 300 \, x + 1\right )} e^{\left (e^{\left (e^{x}\right )} + 1\right )} + 1500 \, x + 10\right )} e^{\left (\frac {1}{5 \, {\left (x e^{\left (e^{\left (e^{x}\right )} + 1\right )} + 10 \, x\right )}}\right )}}{x^{5} e^{\left (2 \, e^{\left (e^{x}\right )} + 2\right )} + 20 \, x^{5} e^{\left (e^{\left (e^{x}\right )} + 1\right )} + 100 \, x^{5}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.19, size = 20, normalized size = 0.77 \begin {gather*} \frac {{\mathrm {e}}^{\frac {1}{50\,x+5\,x\,\mathrm {e}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}}}}{x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.93, size = 20, normalized size = 0.77 \begin {gather*} \frac {e^{\frac {2}{10 x e^{e^{e^{x}} + 1} + 100 x}}}{x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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